73 lines
3.3 KiB
Mathematica
73 lines
3.3 KiB
Mathematica
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function generate_rb_regressor(path_to_urdf)
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% ---------------------------------------------------------------------
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% The function generates regressor for UR10E. It assumes that links of
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% the robot are rigid bodies. Thus the inverse dynamics can be written
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% in linear-in-parameters from: tau = Y(q, dq, ddq) pi
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% ---------------------------------------------------------------------
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% Parse urdf to get robot description
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ur10 = parse_urdf(path_to_urdf);
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% Create symbolic generilized coordiates, their first and second deriatives
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q_sym = sym('q%d',[6,1],'real');
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qd_sym = sym('qd%d',[6,1],'real');
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q2d_sym = sym('q2d%d',[6,1],'real');
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% ------------------------------------------------------------------------
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% Getting gradient of energy functions, to derive dynamics
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% ------------------------------------------------------------------------
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T_pk = sym(zeros(4,4,6)); % transformation between links
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w_kk(:,1) = sym(zeros(3,1)); % angular velocity k in frame k
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v_kk(:,1) = sym(zeros(3,1)); % linear velocity of the origin of frame k in frame k
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g_kk(:,1) = sym([0,0,9.81])'; % vector of graviatational accelerations in frame k
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p_kk(:,1) = sym(zeros(3,1)); % origin of frame k in frame k
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for i = 1:6
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jnt_axs_k = str2num(ur10.robot.joint{i}.axis.Attributes.xyz)';
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% Transformation from parent link frame p to current joint frame
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rpy_k = sym(str2num(ur10.robot.joint{i}.origin.Attributes.rpy));
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R_pj = RPY(rpy_k);
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R_pj(abs(R_pj)<sqrt(eps)) = sym(0); % to avoid numerical errors
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p_pj = str2num(ur10.robot.joint{i}.origin.Attributes.xyz)';
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T_pj = sym([R_pj, p_pj; zeros(1,3), 1]); % to avoid numerical errors
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% Tranformation from joint frame of the joint that rotaties body k to
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% link frame. The transformation is pure rotation
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R_jk = Rot(q_sym(i),sym(jnt_axs_k));
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p_jk = sym(zeros(3,1));
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T_jk = [R_jk, p_jk; sym(zeros(1,3)),sym(1)];
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% Transformation from parent link frame p to current link frame k
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T_pk(:,:,i) = T_pj*T_jk;
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z_kk(:,i) = sym(jnt_axs_k);
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w_kk(:,i+1) = T_pk(1:3,1:3,i)'*w_kk(:,i) + sym(jnt_axs_k)*qd_sym(i);
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v_kk(:,i+1) = T_pk(1:3,1:3,i)'*(v_kk(:,i) + cross(w_kk(:,i),sym(p_pj)));
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g_kk(:,i+1) = T_pk(1:3,1:3,i)'*g_kk(:,i);
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p_kk(:,i+1) = T_pk(1:3,1:3,i)'*(p_kk(:,i) + sym(p_pj));
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beta_K(i,:) = [sym(0.5)*w2wtlda(w_kk(:,i+1)),...
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v_kk(:,i+1)'*vec2skewSymMat(w_kk(:,i+1)),...
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sym(0.5)*v_kk(:,i+1)'*v_kk(:,i+1)];
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beta_P(i,:) = [sym(zeros(1,6)), g_kk(:,i+1)',...
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g_kk(:,i+1)'*p_kk(:,i+1)];
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end
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% ---------------------------------------------------------------------
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% Dynamic regressor of the full paramters
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% ---------------------------------------------------------------------
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beta_Lf = [beta_K(1,:) - beta_P(1,:), beta_K(2,:) - beta_P(2,:),...
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beta_K(3,:) - beta_P(3,:), beta_K(4,:) - beta_P(4,:),...
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beta_K(5,:) - beta_P(5,:), beta_K(6,:) - beta_P(6,:)];
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dbetaLf_dq = jacobian(beta_Lf,q_sym)';
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dbetaLf_dqd = jacobian(beta_Lf,qd_sym)';
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tf = sym(zeros(6,60));
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for i = 1:6
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tf = tf + diff(dbetaLf_dqd,q_sym(i))*qd_sym(i)+...
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diff(dbetaLf_dqd,qd_sym(i))*q2d_sym(i);
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end
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Y_f = tf - dbetaLf_dq;
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% Generate function from a symbolic expression for the regressor
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matlabFunction(Y_f,'File','autogen/standard_regressor_UR10E',...
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'Vars',{q_sym,qd_sym,q2d_sym});
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